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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 193

Consider this equation

Where n is an even number, Pi is the consecutive prime and Ps is the resulting prime.

Some of the primes

Let P1=2 and n=4

Ps={193, 227}

Let P1=2 and n=6

Ps={29989, 30071}

Let P1=3 and n=2

Ps={7, 23}

Let P1=3 and n=4

Ps={1129, 1181}

Let P1=5 and n=2

Ps={23, 47}

Let P1=5 and n=6

Ps={1616543, 1616687}

*Last edited by Stangerzv (2013-06-04 23:50:25)*

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 193

I think I could rearrange the equation to avoid negative prime. Below is the modified version.

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**barbie19022002****Member**- Registered: 2013-05-24
- Posts: 1,314

did you make this equation yourself..?

Jake is Alice's father, Jake is the ________ of Alice's father?

Why is T called island letter?

think, think, think and don't get up with a solution...

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 193

Yep barbie19022002..I kinda like prime numbers and I do lots of thinking about them. Most of the prime numbers I listed here were not known to me before and this prime formula was developed this morning. I got to know about prime numbers through my formulation of sums of power for arithmetic progression. I got involved in prime numbers after trying to link my sums of power formulation with Riemann's zeta function. Sometimes, it is a frustration to know that someone else had found it but it is kool to find something without knowing it beforehand.

*Last edited by Stangerzv (2013-06-05 03:07:39)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,562

Hi;

Seems that for P1 = 2 that they are very rare.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

Here are some (unconfirmed):

P1 n

2, 4

2, 6

5, 4

5, 8

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 193

hi bobbym

There are three things that the prime has to match, a product, a sum and +- and when n becoming larger it would be harder to find the prime. This is what I believe and maybe a computational result would give a slightly different picture.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,562

There are no solutions with P1=2 and n < =1000 other than n = 4 and n = 6. These are already 3300 digit numbers!

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 193

New update

P1=13 and n=2

Ps={191, 251}

P1=43 and n=2

Ps={1931, 2111}

*Last edited by Stangerzv (2013-06-05 03:25:13)*

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 193

Hi bobbym

I had a feeling it would be hard to find prime for n>6 for P1=2 and I quit looking for them and now knowing there is no prime for n up to 1000 it is just worthy not trying:)

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,562

There are no solutions with P1=3 and n < = 1000 other than n = 2 and n = 4.

For P1=5 and n < = 1000 other than n = 2 and n = 6, I can find no others.

For P1=7 and n < = 1000, I can find no solutions.

For P1=11 and n < = 1000, I can find no solutions.

For P1=13 and n < = 1000 other than n = 2, I can find no others.

For P1=17 and n < = 1000, I can find no solutions.

For P1=19 and n < = 1000, I can find no solutions.

For P1=23 and n < = 1000, I can find no solutions.

For P1=29 and n < = 1000, I can find no solutions.

For P1=31 and n < = 1000, I can find no solutions.

For P1=37 and n < = 1000, I can find no solutions.

For P1=41 and n < = 1000, I can find no solutions.

For P1=43 and n < = 1000 other than n = 2, I can find no others.

For P1=47 and n < = 1000, I can find no solutions.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

Let P1=2 and n=4

Ps={193, 227}

How are you getting this? It seems I have misread something...

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,915

Hi stefy,

P1 is the first prime in the sequence, and n is the number of primes in the sequence.

P1=2, n=4

2+3+5+7=17

2*3*5*7=210

210-17=193

210+17=227

Ps={193,227}

P1=3,n=2

3+5=8

3*5=15

15-8=7

15+8=23

Ps={7,23}

*Last edited by phrontister (2013-06-05 05:27:52)*

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

Ah, got it. Didn't subtract 1 in the upper summation bound.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,915

Testing for n<=100, I found many solutions up to P1=50929, most of which are for n=2. There are some n=4, 6 and 8, and several loners: n=14, 22, 26 and 56.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

Hi

For P1<=p_10000 there is nothing for 34<=n<=54 and 58<=n<=68.

Also did a search for (P1,n) pairs where P1 can go up to p_100000 and 34<=n<=68.

*Last edited by anonimnystefy (2013-06-05 10:22:38)*

Here lies the reader who will never open this book. He is forever dead.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,915

The result with the highest n I've got so far is P=61001, n=154.

Backwards check (in M), where e1 and e2 are the two absolute +/- Ps elements:

Input: a = FactorInteger[(e1 + e2)/2]; {First[First[a]], Length[a]}

Output: {61001,154}

My code looks a bit clunky with the repeat "First[First", but it works and I don't know how to improve it.

Prime factor range is 61001 to 62761, which comprises 154 primes. 61001 and 62761 are the 6146th and 6299th primes (respectively), but I don't know how that information can be used.

*Last edited by phrontister (2013-06-06 04:42:51)*

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 193

It seems there are plenty of these primes with an exception that most of them occur at smaller value of n.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,915

Yes, it's rarefied air up there for higher numbers.

I tried for P1=7, got to n=7350 with no result, and pulled the plug.

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